Brief window of query failures immediately after a server pod finishes restarting and becomes healthy

We regularly experience a brief window of query failures immediately after a Pinot server pod transitions to a healthy state following a restart. Notably, there is no observed disruption during the initial termination phase or while the pod is in a 0/1 Runningstate; the instability occurs specifically as the service becomes ready to handle traffic again.

We have been seeing this issue for quite some time. We would appreciate if we can get guidance over this issue.

### Error Details

The failures manifest as QueryExecutionError exceptions (likely caused by gRPC connection timeouts). The logs indicate that the query dispatcher is unable to establish a connection to the newly restarted pod.

Full Java Stack Trace:

```
QueryExecutionError: Error dispatching query: 667717545000000055 to server: pinot-server-8.pinot-server-headless.pinot.svc.cluster.local@{8421,8442}
at org.apache.pinot.query.service.dispatch.QueryDispatcher.processResults(QueryDispatcher.java:689)
at org.apache.pinot.query.service.dispatch.QueryDispatcher.execute(QueryDispatcher.java:643)
at org.apache.pinot.query.service.dispatch.QueryDispatcher.submit(QueryDispatcher.java:584)
at org.apache.pinot.query.service.dispatch.QueryDispatcher.submitAndReduce(QueryDispatcher.java:219)
Caused by: io.grpc.StatusRuntimeException: UNAVAILABLE: io exception
at io.grpc.Status.asRuntimeException(Status.java:532)
at io.grpc.stub.ClientCalls$StreamObserverToCallListenerAdapter.onClose(ClientCalls.java:581)
at io.grpc.internal.ClientCallImpl.closeObserver(ClientCallImpl.java:566)
at io.grpc.internal.ClientCallImpl.access$100(ClientCallImpl.java:72)
at io.grpc.internal.ClientCallImpl$ClientCallListenerImpl.onClose(ClientCallImpl.java:547)
at io.grpc.internal.ClientCallImpl.closeObserver(ClientCallImpl.java:566)
at io.grpc.internal.ClientCallImpl.access$100(ClientCallImpl.java:72)
at io.grpc.internal.ClientCallImpl$ClientStreamListenerImpl$1StreamClosed.runInternal(ClientCallImpl.java:739)
at io.grpc.internal.ClientCallImpl$ClientStreamListenerImpl$1StreamClosed.runInContext(ClientCallImpl.java:720)
at io.grpc.internal.ContextRunnable.run(ContextRunnable.java:37)
at io.grpc.internal.SerializingExecutor.run(SerializingExecutor.java:133)
at java.base/java.util.concurrent.ThreadPoolExecutor.runWorker(ThreadPoolExecutor.java:1136)
at java.base/java.util.concurrent.ThreadPoolExecutor$Worker.run(ThreadPoolExecutor.java:635)
at java.base/java.lang.Thread.run(Thread.java:840)
Caused by: java.io.IOException: connection timed out after 30000 ms: pinot-server-8.pinot-server-headless.pinot.svc.cluster.local/100.64.62.48:8421
at io.grpc.netty.shaded.io.netty.channel.epoll.AbstractEpollChannel$AbstractEpollUnsafe$2.run(AbstractEpollChannel.java:615)
at io.grpc.netty.shaded.io.netty.util.concurrent.PromiseTask.runTask(PromiseTask.java:98)
at io.grpc.netty.shaded.io.netty.util.concurrent.ScheduledFutureTask.run(ScheduledFutureTask.java:160)
at io.grpc.netty.shaded.io.netty.util.concurrent.AbstractEventExecutor.runTask(AbstractEventExecutor.java:173)
at io.grpc.netty.shaded.io.netty.util.concurrent.AbstractEventExecutor.safeExecute(AbstractEventExecutor.java:166)
at io.grpc.netty.shaded.io.netty.util.concurrent.SingleThreadEventExecutor.runAllTasks(SingleThreadEventExecutor.java:470)
at io.grpc.netty.shaded.io.netty.channel.epoll.EpollEventLoop.run(EpollEventLoop.java:384)
at io.grpc.netty.shaded.io.netty.util.concurrent.SingleThreadEventExecutor$4.run(SingleThreadEventExecutor.java:997)
at io.grpc.netty.shaded.io.netty.util.internal.ThreadExecutorMap$2.run(ThreadExecutorMap.java:74)
at java.base/java.lang.Thread.run(Thread.java:840)
```

### Environment Context
Pinot Version: 1.5.0
EKS 1.34

Start with QueryDispatcher.java, especially processResults, execute, submit, and submitAndReduce, then examine the server readiness and traffic transition in the EKS 1.34 deployment. Reproduce the failure on Pinot 1.5.0 during a server pod restart; done means queries no longer fail with gRPC connection timeouts after the pod becomes healthy.

Written by the indexing model from the issue text.